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Given an action of a group Γ on a measure space X, we provide a criterion under which two sets A, B ⊂ X are measurably equidecomposable, i.e. A can be partitioned into finitely many measurable pieces, which can be rearranged using the elements of Γ to form a partition of B.In particular, we show that every bounded measurable subset of R n , n 3, with non-empty interior is measurably equidecomposable to a ball. Similar result holds e.g. for measurable subsets of the unit sphere S n−1 .

This paper analyzes the energy efficiency of a Micro Fiber Composite (MFC) piezoelectric system. It is based on a smart Lead Zirconate Titanate material that consists of a monolithic PZT (piezoelectric ceramic) wafer, which is a ceramic-based piezoelectric material. An experimental test rig consisting of a wind tunnel and a developed measurement system was used to conduct the experiment. The developed test rig allowed changing the air velocity around the tested bluff body and the frequency of forced vibrations as well as recording the output voltage signal and linear acceleration of the tested object. The mechanical vibrations and the air flow were used to find the optimal performance of the piezoelectric energy harvesting system. The performance of the proposed piezoelectric wind energy harvester was tested for the same design, but of different masses. The geometry of the hybrid bluff body is a combination of cuboid and cylindrical shapes. The results of testing five bluff bodies for a range of wind tunnel air flow velocities from 4 to 15 m/s with additional vibration excitation frequencies from 0 to 10 Hz are presented. The conducted tests revealed the areas of the highest voltage output under specific excitation conditions that enable supplying low-power sensors with harvested energy.

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